The actual crown is the slight bevel right where the rifling ends.
The purpose is to insure there are no burrs or other imperfections left by the machining process.

The end of the muzzle, often called the crown, may or may not have a real effect on accuracy.
Remington believes their spherical muzzles enhance accuracy.
Older types of muzzles are mostly to protect the rifling by recessing it in one way or another.